You are half right. Get up and wake up depends on the situation how they are used. 'Get up' and 'wake up' are synonyms like उठना and जागना in hindi but they share the same meaning only when we are talking about sleep. As you can say मैं नींद से उठ गया (I got up from sleep) or मैं नींद से जाग गया (I woke up from sleep) both are same in meaning. But when the word उठना is mentioned we will use the word 'get up' not 'wake up'. The word 'get' has many meanings in Hindi as it has in English like अपनी जगह से उठ जाओ (get up from your place) बाहर जाओ (get out) क्या आपको कुछ मिला है (have you get anything) and so on. Therefore, उठो means 'get up' and जागो means 'wake up'. Hence proved.
The two phrasal verbs 'get up' and 'wake up' sounds similar, but having a different meaning , as well as context driven. When your alarm rings in the morning you 'wake up' (जागना) as you are no longer sleeping. 'Get up' (उठना) means that you get out of bed. 'I wake up at 7am, but i don't get up until 7:30.
Um well in conversation it really doesn't matter imo. "What time did you wake up" vs "what time did you get up" means exactly the same thing... nobody makes such technical distinctions.
You could say "तुम जागकर उठते हो" to really hammer the difference but nobody says that and its just being pedantic.
Plus check this https://translate.google.com/#en/hi/wake%20up wake up = उठो
I'm still not convinced. Both "get up" and "wake up" should be accepted.
BUT if we're going to maintain this pedantic distinction then examine the common Hindi/Urdu phrase "Utho aur Jago" - as it appears in the title of a book by Swami Vivekananda and is also the name of a morning show in Pakistan. According to you, you can't get up without waking up first so here "Utho" means "Wake up" and "Jago" means "Get up" - which in turn makes the translation of the sentence in question here "ये लोग पाँच बजे जागते हैं।" - "These people get up at five" and "These people wake up at five" is then completely incorrect.